Funky Functional Equation Part II

Algebra Level 5

Find the absolute value of the product of the two possible values for f(10)f(10) given that

f(xf(x)+f(y))=y+f(x)2f(xf(x)+f(y))=y+f(x)^2

where x,yRx, y \in \mathbb{R} and f(x)f(x) is a polynomial function.


Note: This question has been edited several times, and is now correct.

See Part I if you enjoyed this problem! :D

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